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Fixed end rotation
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The structure is a simple beam girder with 1 to 3 spans and constant cross-section and constant mass intensity in longitudinal direction. The structure is at all support points rigidly supported in vertical and lateral direction. Rigid rotational constraints are applied at the begin and end of the structure. The longitudinal support direction is at the begin of the structure. The model with clamped ends also allows for approximately analyzing frame structures. |
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Length
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Total length of the structural system. In the case of girders with 2 or 3 spans, the individual span lengths are implicitely computed from the subdivision information L1, L2, L3. I.e. the element lengths of the system are constant. For instance, for calculating a 2 span girder with 10.0 m and 7.5 m spans, L1 must be set to 20 and L2 to 15. All elements will then have a length of 0.5 m, and the intermediate support is arranged after the 20th element. |
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L1 - Subdivision
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Number of Elements in the first span. |
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L2 - Subdivision
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Number of Elements in the 2nd span (Zero = only one span exists). |
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L3 - Subdivision
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Number of Elements in the 3rd span (Zero = only one or two spans exist). |
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Begin ramp
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Length of the region, where a load becomes gradually effective at the first node while it approaches the begin of the bridge. This avoids the consideration of sudden impacts causing unrealistic results. |
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End ramp
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Length of the region, where a load gradually looses its effect on the last node after it has left the bridge structure. This avoids the consideration of sudden impacts causing unrealistic results. |
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Bridge Mass
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Weight of the bridge structure per length unit in kN/m (for the specification of the mass). Note: The mass definition is done by specifying respective weights. The conversion to mass quantities is done with using the fix value 9.81 m/s2 as gravity constant.
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Ballast Mass
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Superimposed dead load per length unit in kN/m (for specification of additional mass). Note: The mass definition is done by specifying respective weights. The conversion to mass quantities is done with using the fix value 9.81 m/s2 as gravity constant.
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E
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Young's modulus of the material of the superstructure The shear modulus is calculated with G=E(2*(1+ny)) with ny=0.2 (torsion). Shear deformation is not considered due to missing definition of shear areas. |
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Ax
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Cross-section area of the girder (shear areas are assumed 0.0). |
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Ix
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Torsional moment of inertia of the cross-section of the girder |
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Iy
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Bending moment of inertia of the cross-section of the girder in lateral direction |
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Iz
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Bending moment of inertia of the cross-section of the girder in vertical direction |
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Damping (%)
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Damping coefficient as percentage of the critical damping Note: The program uses Rayleigh damping, where the damping matrix is a linear combination of the stiffness matrix and the mass matrix (C = alpha*M + beta*K). In this approach, the equivalent damping ratio is varying with the frequency. The coefficients alpha and beta are calculated in the program such that the given damping ratio is exact for the angular frequencies w1 and w2 (in rad/s). Modes with frequencies between these values are slightly less damped, those with frequencies outside this region are damped to a higher extent.
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w1(rad/s), w2(rad(s)
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Relevant angular frequencies for calculating the Rayleigh damping coefficients. w1 shall be the first relevant Eigenfrequency, w2 the 2nd relevant frequency. Damping assumption is on the save side if the value of w2 related to a higher frequency. Default: w1=61, w2=157 (10.0 and 25 Hz)
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